We discuss constraints on cosmic reionisation and their implications on a cosmic SFR density $rho_mathrm{SFR}$ model; we study the influence of key-parameters such as the clumping factor of ionised hydrogen in the intergalactic medium (IGM) $C_{H_{II}}$ and the fraction of ionising photons escaping star-forming galaxies to reionise the IGM $f_mathrm{esc}$. Our analysis uses SFR history data coming from luminosity functions, assuming that star-forming galaxies were sufficient to lead the reionisation process at high redshift. We add two other sets of constraints: measurements of the IGM ionised fraction and the most recent result from Planck Satellite about the integrated Thomson optical depth of the Cosmic Microwave Background (CMB) $tau_mathrm{Planck}$. We also consider various possibilities for the evolution of these two parameters with redshift, and confront them with observational data cited above. We conclude that, if the model of a constant clumping factor is chosen, the fiducial value of $3$ often used in papers is consistent with observations; even if a redshift-dependent model is considered, the resulting optical depth is strongly correlated to $C_{H_{II}}$ mean value at $z>7$, an additional argument in favour of the use of a constant clumping factor. Besides, the escape fraction is related to too many astrophysical parameters to allow us to use a complete and fully satisfactory model. A constant value with redshift seems again to be the most likely expression: considering it as a fit parameter, we get from the maximum likelihood (ML) model $f_mathrm{esc}=0.24pm0.08$; with a redshift-dependent model, we find an almost constant evolution, slightly increasing with $z$, around $f_mathrm{esc}=0.23$. Last, our analysis shows that a reionisation beginning as early as $zgeq14$ and persisting until $zsim6$ is a likely storyline.
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